A numerical approach for the stochastic control of a two-level quantum system
The aim of this paper is to study the problem of controlling the stochastic evolution of a two-level quantum system in the presence of two randomly fluctuating electromagnetic fields, given by a Wiener process. The system is modeled by the stochastic Schr¨odinger equation dependent on time. We set up the quantum optimal control problem by choosing a cost functional type Bolza.
By applying the Pontryagin Maximum Stochastic Principle to an extended Hamiltonian, we express the stochastic optimal controls in terms of the co-state of the system. To solve numerically the resulting stochastic differential equations we propose an iterative algorithm using the Euler-Maruyama method. Finally, we obtain the optimal trajectories on the Bloch sphere.
CYBERNETICS AND PHYSICS, Vol. 9, No. 2. 2020, 107–116. https://doi.org/10.35470/2226-4116-2020-9-2-107-116